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The exact solutions of the variable-order fractional stochastic Ginzburg–Landau equation along with analysis of bifurcation and chaotic behaviors

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Listed:
  • Qi, Jianming
  • Li, Xinwei
  • Bai, Leiqiang
  • Sun, Yiqun

Abstract

This article explores the exact solutions of the variable order fractional derivative of the stochastic Ginzburg–Landau equation (GLE) using the G′G2-expansion method with the assistance of Matlab R2021a software. The paper presents three key aspects that contribute to its novelty: (1) Our study introduces and examines the variable order fractional derivative of the stochastic Ginzburg–Landau equation (VOFDSGLE) for the first time, demonstrating our best cognitive effort. We successfully obtain a significant number of exact solutions and provide illustrative examples and visual representations of the VOFDSGLE. These obtained solutions have the potential to offer enhanced availability and practicality in understanding the mechanisms behind the complex physical phenomena observed in various fields. (2) Additionally, we investigate the phase portraits of the variable-order fractional stochastic Ginzburg–Landau equation under a specific condition. We analyze the associated sensitivity and chaotic behaviors, which have not been examined in prior studies on stochastic Ginzburg–Landau equation (Mohammed et al., 2021; Alhojilan and Ahmed, 2023). This exploration adds a unique contribution to the existing literature and offers valuable insights into the dynamics of the system. (3) Our numerical observations underscore the significant impact of multiplicative noise on the solutions. The progressive degradation of patterns and the tendency towards planar surfaces indicate the disruption caused by increasing noise intensity. Moreover, the convergence of solution magnitudes to zero underlines the stabilizing influence of the multiplicative noise. Furthermore, we advance the existing knowledge regarding the response of the stochastic GLE model to small noise, offering valuable insights into the system’s transition behaviors in the energy landscape.

Suggested Citation

  • Qi, Jianming & Li, Xinwei & Bai, Leiqiang & Sun, Yiqun, 2023. "The exact solutions of the variable-order fractional stochastic Ginzburg–Landau equation along with analysis of bifurcation and chaotic behaviors," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    • Handle: RePEc:eee:chsofr:v:175:y:2023:i:p2:s0960077923008470
    DOI: 10.1016/j.chaos.2023.113946
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    References listed on IDEAS

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    1. Nguyen Tien, Dung, 2013. "A stochastic Ginzburg–Landau equation with impulsive effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(9), pages 1962-1971.
    2. Alquran, Marwan & Yousef, Feras & Alquran, Farah & Sulaiman, Tukur A. & Yusuf, Abdullahi, 2021. "Dual-wave solutions for the quadratic–cubic conformable-Caputo time-fractional Klein–Fock–Gordon equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 62-76.
    3. Hong Lu & Linlin Wang & Mingji Zhang, 2022. "Dynamics of Fractional Stochastic Ginzburg–Landau Equation Driven by Nonlinear Noise," Mathematics, MDPI, vol. 10(23), pages 1-36, November.
    4. Muhammad Arshad & Aly R. Seadawy & Dianchen Lu, 2017. "Bright–dark solitary wave solutions of generalized higher-order nonlinear Schrödinger equation and its applications in optics," Journal of Electromagnetic Waves and Applications, Taylor & Francis Journals, vol. 31(16), pages 1711-1721, November.
    5. Shao-Wen Yao & Esin Ilhan & P. Veeresha & Haci Mehmet Baskonus, 2021. "A Powerful Iterative Approach For Quintic Complex Ginzburg–Landau Equation Within The Frame Of Fractional Operator," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(05), pages 1-13, August.
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    Cited by:

    1. Çelik, Nisa & Tetik, Duygu, 2024. "New dynamical analysis of the exact traveling wave solutions to a (3+1)-dimensional Gardner-KP equation by three efficient architecture," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).

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